The sum of three numbers is 102 . the third number is 4 times the first. the first number is 6 more than the second. what are the numbers?

To solve this problem, let us first assign some variables. Let us say that the numbers are:

x = the variable representing the first number

y = the variable representing the second number

z = the variable representing the third number

From the given problem, we know that:

x + y + z = 102                    ---> 1

z = 4 x                                    ---> 2

x = y + 6                                ---> 3

Rewriting equation 3 in terms of y:

y = x – 6                                ---> 4

Combining equations 1, 2 and 4 to express solely on x:

x + (x – 6) + (4 x) = 102

6 x – 6 = 102

6 x = 108

x = 18

From equation 2:

z = 4 (18)

z = 72

From equation 4:

y = 18 – 6

y = 12

Hence, the numbers are:

x = 18

y = 12

z = 72